I have some problems when I have to derive: I don't know where I have to begin and where I have to stop. For example, if I have $$f(x)=(x^2 +1)(x^2 +3)$$ I know that I have to use the product rule so I get $$f'(x)=(x^2 +1)'(x^2 +3)+(x^2 +1)(x^2 +3)'$$ and the resolution is $$f'(x)=4x^3 +8x$$. But why can't I derive the stuff inside the brackets, like $$f(x)'=(2x)(2x)$$ and then $$f'(x)=4x^2$$
And I always have that problem, I don't know what rule I should use first. Thank you.